SOLUTION: three good friends are in the same algebra class. their scores on a recent test are three consecutive odd integers whose sum is 219. find each score

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Question 1094637: three good friends are in the same algebra class. their scores on a recent test are three consecutive odd integers whose sum is 219. find each score
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the consecutive odd integers be
+n+, +n%2B2+, and +n%2B4+
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+n+%2B+n+%2B+2+%2B+n+%2B+4+=+219+
+3n+%2B+6+=+219+
+3n+=+213+
+n+=+71+
and
+n+%2B+2+=+73+
+n+%2B+4+=+75+
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The consecutive odd numbers are 71,73, and 75
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check:
+71+%2B+73+%2B+75+=+219+
+219+=+219+

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Here is a good time saver for solving problems like this.

Since the scores are consecutive odd integers, the score in the middle is the average of the three scores.

In your problem you know the sum of the three scores is 219, so the average is 219/3 = 73. That means the middle score is 73, making the other two scores 71 and 75.

The lesson to be learned: in a sequence with an odd number of terms, often letting x be the middle number is a lot easier than letting x be the first number.